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I need help with that sum $$\sum_{k=1}^N \csc^2\left(\frac{k\pi}{2N}\right)$$ - it is given in many tables as a standard result, but I can't figure it out. I know how to do $\sin^2$ and $\cos^2$, but the method I am using (multiplying by some half angle function like $\sin\left(\frac{\pi}{4N}\right)$) doesn't seem to work. I also tried splitting in $1+\cot^2$ but the half angle formula for $\cot$ is not nice.

Any hints will be appreciated.

ThunderBiggi
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    See http://math.stackexchange.com/questions/544228/finite-sum-sum-k-1m-1-frac1-sin2-frack-pim OR http://math.stackexchange.com/questions/1590931/how-prove-frac1-sin2-frac-pi2n-frac1-sin2-frac2-pi2n – lab bhattacharjee Oct 05 '16 at 12:21
  • Thank you very much! Is there a way to search for LaTeX expressions in the titles? – ThunderBiggi Oct 05 '16 at 14:50
  • Have a look at https://en.wikipedia.org/wiki/Basel_problem#The_proof and http://math.stackexchange.com/questions/1935407/how-to-prove-that-sum-k-1-n-frac-1-1-cos-frac-k-pi-n-frac-2n2/1936382#1936382 – Jack D'Aurizio Oct 05 '16 at 17:39
  • @user1482714 I think you just type out the $\LaTeX$ because the search doesn't consider rendered $\LaTeX$ in posts, but the unrendered versions. – Simply Beautiful Art Oct 07 '16 at 01:23
  • @SimpleArt Ok, I will try this the next time – ThunderBiggi Oct 07 '16 at 12:53

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